AP 微積分BC 選擇題樣卷一

1、AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions - 55 Minutes1) Given Find dy/dx.a) b) c) d) e) 2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x =

2、1 and x = e, about the y-axis.a) b) c) d) e) 3) The graph of the derivative of f is shown below. Find the area bounded between the graph of f and the x-axis over the interval -2,1, given that f(0) = 1.a) b) c) d) e) 4) Determine dy/dt, given that and a) b) c) d) e) 5) The function is invertible. Giv

3、e the slope of the normal line to the graph of f -1 at x = 3. a) b) c) d) e) 6) Determine a) b) c) d) e) 7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ). a) b) c) d) e) 8) Determine a) b) c) d) e) 9) Determine a) b) c) d) e) 10) Give the radius of convergence for th

4、e series a) b) c) d) e) 11) Determine a) b) c) d) e) 12) The position of a particle moving along the x-axis at time t is given by At which of the following values of t will the particle change direction? I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III an

5、d IVe) III and IV13) Determine a) b) c) d) e) 14) Determine the y-intercept of the tangent line to the curve at x = 4.a) b) c) d) e) 15) The function f is graphed below. Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval 2,5.a) b) c)

6、d) e) 16) Give the average value of the function on the interval 1,3.a) b) c) d) e) 17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the h

7、eight is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.a) b) c) d) e) 18) The graph of the derivative of f is shown below. Give the number of values of x in the interval -3,3 where the graph of f has inflection.a) b) c) d) e) 19) A rectangle has its base on the x-axis

8、and its vertices on the positive portion of the parabola What is the maximum possible area of this rectangle?a) b) c) d) e) 20) Compute a) b) c) d) e) 21) Determine a) b) c) d) e) 22) Determine a) b) c) d) e) 23) Give the exact value of a) b) c) d) e) 24) Determine a) b) c) d) e) 25) Give the deriva

9、tive of a) b) c) d) e) 26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function a) b) c) d) e) 27) Determine a) b) c) d) e) 28) Which of the following series converge(s)? a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d) 2) e) 3) b) 4) b) 5) e) 6) a) 7) c) 8)